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Statements
U
(
a
,
b
,
z
)
=
(
-
1
)
n
z
1
-
b
-
n
Γ
(
1
+
a
-
b
)
∫
0
∞
𝐌
(
b
-
a
,
b
,
t
)
e
-
t
t
b
+
n
-
1
t
+
z
d
t
,
Kummer-confluent-hypergeometric-U
𝑎
𝑏
𝑧
superscript
1
𝑛
superscript
𝑧
1
𝑏
𝑛
Euler-Gamma
1
𝑎
𝑏
superscript
subscript
0
Kummer-confluent-hypergeometric-bold-M
𝑏
𝑎
𝑏
𝑡
superscript
𝑒
𝑡
superscript
𝑡
𝑏
𝑛
1
𝑡
𝑧
𝑡
{\displaystyle{\displaystyle U\left(a,b,z\right)=\frac{(-1)^{n}z^{1-b-n}}{%
\Gamma\left(1+a-b\right)}\int_{0}^{\infty}\frac{{\mathbf{M}}\left(b-a,b,t%
\right)e^{-t}t^{b+n-1}}{t+z}\mathrm{d}t,}}
|
ph
z
|
<
π
phase
𝑧
𝜋
{\displaystyle{\displaystyle\left|\operatorname{ph}z\right|<\pi}}
-
ℜ
b
<
n
<
1
+
ℜ
(
a
-
b
)
𝑏
𝑛
1
𝑎
𝑏
{\displaystyle{\displaystyle-\Re b<n<1+\Re(a-b)}}
|
ph
z
|
<
π
ph
𝑧
𝜋
{\displaystyle{\displaystyle\left|\operatorname{ph}z\right|<\pi}}
n
=
0
,
1
,
2
,
…
𝑛
0
1
2
…
{\displaystyle{\displaystyle n=0,1,2,\dots}}
-
ℜ
b
<
n
<
1
+
ℜ
(
a
-
b
)
𝑏
𝑛
1
𝑎
𝑏
{\displaystyle{\displaystyle-\Re b<n<1+\Re(a-b)}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
U
(
a
,
b
,
z
)
Kummer-confluent-hypergeometric-U
𝑎
𝑏
𝑧
{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
𝐌
(
a
,
b
,
z
)
Kummer-confluent-hypergeometric-bold-M
𝑎
𝑏
𝑧
{\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right%
)}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
∫
{\displaystyle{\displaystyle\int}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
n
𝑛
{\displaystyle{\displaystyle n}}
z
𝑧
{\displaystyle{\displaystyle z}}
Identifiers
